Consistent treatment for a single electron in a thermal crystal with an applied electric field

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Abstract
We investigate a single electron drifting in a thermal crystal under an applied electric field. With the help of the path-integral approach of the nonequilibrium Green’s function, we treat the electron drift motion and the fluctuation in a consistent way in which the balance of momentum is consistent with the balance of energy. We treat the applied field and the electron-phonon interaction nonperturbatively, so that the high-field effect as well as the quantum interference effect have been taken into account. We derive a set of coupled equations which consistently describe the drift motion and the fluctuation of the electron. By solving these equations we obtain (1) the nonlinear relation between the drift velocity and applied electric field which confirms the Thornber-Feynman prediction of the threshold for the stable steady-transport state; (2) the effective electron temperatures, the nonequilibrium noise, and the distribution functions.